Because of the requirements to keep the in and out conductors separated. you often have to run one of conductors from the old location to the new location and the second set of conductors from the new location directly to the next device on the circuit.
Yes this work will cause a trouble signal, you should not have to shut the system down just acknowledge / silence the trouble indicator.
You also have to make sure any entity that monitors the fire system is aware you are working on it or they may dispatch a service tech to the site to see the what the trouble is.
In my area some fire departments dispatch a truck (slow, no rush) to troubles or supervisory conditions on a fire system.
(This can be a bit of a problem if maybe you did not get a permit to work on the system first.

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This type of work and especially in a facility like a hospital tends to eat up a lot of time for little real progress.
You may want to call the hospitals facility engineer and see what they have to say about touching the fire alarm system. In some cases they will have a contract with a service company that either has to be on site to look at the changes or might even have to do the work.
For instance at a large shopping mall we moved and added some devices and the names of the tenant changed so the panel need some small programing changes.
We moved the devices, ran all the new wiring back to a fire alarm terminal cabinet and then we had to hire the malls fire alarm contractor to shut the panel down, change the programing to indicate the new tenant names (10 minutes tops) and then they tied the wires in we left for them in the terminal cabinet, again maybe ten minutes. Test the system and leave. This other contractor on site for maybe 90 minutes.
Cost to us $1,800.